An animal breeder can buy four types of food for Vietnamese pot-bellied pigs. Each case of Brand A contains 35 units of fiber, 40 units of protein, and 40 units of fat. Each case of Brand B contains 140 units of fiber, 120 units of protein, and 120 units of fat. Each case of Brand C contains 245 units of fiber, 200 units of protein, and 220 units of fat. Each case of Brand D contains 420 units of fiber, 360 units of protein, and 340 units of fat.
How many cases of each brand should the breeder mix together to obtain a food that provides 4305 units of fiber, 3600 units of protein, and 3780 units of fat? Let x represent the number of cases of brand A, y represent cases of brand B, z represent the cases of brand C, and w represent the number of cases of brand D. There are 4 ways in which the breeder can mix brands to obtain a food that provides 4305 units of fiber, 3600 units of protein, and 3780 units of fat.
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